The album peaked at #164 on the Billboard Pop Albums and 200 albums charts. In 1989, Spin named Swordfishtrombones the second greatest album of all time.[4] In 2006, Q placed the album at #36 in its list of "40 Best Albums of the '80s."[5]

Pitchfork Media listed Swordfishtrombones as 11th best album of the 1980s. Slant Magazine listed the album at #26 on its list of "Best Albums of the 1980's".[6]